The operating theater is one of the most expensive units in the hospital, representing up to 40% of the total expenses. Because of its importance, the operating room scheduling problem has been addressed from many different perspectives since the early 1960s. One of the main difficulties that has reduced the applicability of the current results is the high variability in surgery duration, making schedule recommendations hard to implement.

In this work, we propose a time-indexed scheduling formulation to solve the operational problem. Our main contribution is that we propose the use of chance constraints related to the surgery duration’s probability distribution for each surgeon to improve the scheduling performance. We show how to implement these chance constraints as linear ones in our time-indexed formulation, enhancing the performance of the resulting schedules significantly.

Through data analysis of real historical instances, we develop specific constraints that improve the schedule, reducing the need for overtime without affecting the utilization significantly. Furthermore, these constraints give the operating room manager the possibility of balancing overtime and utilization through a tunning parameter in our formulation. Finally, through simulations and the use of real instances, we report the performance for four different metrics, showing the importance of using historical data to get the right balance between the utilization and overtime.

手术室是医院最昂贵的单位之一，占总费用的 40%。由于其重要性，自 1960 年代初以来，手术室调度问题已从许多不同的角度得到解决。降低当前结果适用性的主要困难之一是手术持续时间的高度可变性，使得计划建议难以实施。

在这项工作中，我们提出了一种时间索引调度公式来解决操作问题。我们的主要贡献是我们建议使用与每个外科医生的手术持续时间概率分布相关的机会约束来提高调度性能。我们展示了如何在我们的时间索引公式中将这些机会约束作为线性约束来实现，从而显着提高结果调度的性能。

通过对真实历史实例的数据分析，我们制定了改进进度的特定约束，减少了加班需求，同时不会显着影响利用率。此外，这些约束使手术室经理可以通过我们公式中的调整参数来平衡加班时间和利用率。最后，通过模拟和真实实例的使用，我们报告了四个不同指标的性能，显示了使用历史数据在利用率和加班时间之间取得适当平衡的重要性。